Transformation collection. More...

Functions
template<typename Derived >
Eigen::Quaternion< typename Derived::Scalar >	NAV::trafo::b_Quat_n (const Eigen::MatrixBase< Derived > &rollPitchYaw)
	Quaternion for rotations from navigation to body frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::b_Quat_n (Scalar roll, Scalar pitch, Scalar yaw)
	Quaternion for rotations from navigation to body frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::b_Quat_p (Scalar mountingAngleX, Scalar mountingAngleY, Scalar mountingAngleZ)
	Quaternion for rotations from platform to body frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::e_Quat_i (Scalar time, Scalar omega_ie=InsConst< Scalar >::omega_ie)
	Quaternion for rotations from inertial to Earth-centered-Earth-fixed frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::e_Quat_n (Scalar latitude, Scalar longitude)
	Quaternion for rotations from navigation to Earth-fixed frame.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::internal::ecef2lla (const Eigen::MatrixBase< Derived > &e_position, typename Derived::Scalar a, typename Derived::Scalar b, typename Derived::Scalar e_squared)
	Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::ecef2lla_GRS80 (const Eigen::MatrixBase< Derived > &e_position)
	Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude using GRS90.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::ecef2lla_WGS84 (const Eigen::MatrixBase< Derived > &e_position)
	Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude using WGS84.

template<typename DerivedA , typename DerivedB >
Eigen::Vector3< typename DerivedA::Scalar >	NAV::trafo::ecef2ned (const Eigen::MatrixBase< DerivedA > &e_position, const Eigen::MatrixBase< DerivedB > &lla_position_ref)
	Converts ECEF coordinates into local NED coordinates.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::i_Quat_e (Scalar time, Scalar omega_ie=InsConst< Scalar >::omega_ie)
	Quaternion for rotations from Earth-centered-Earth-fixed to inertial frame.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::internal::lla2ecef (const Eigen::MatrixBase< Derived > &lla_position, typename Derived::Scalar a, typename Derived::Scalar e_squared)
	Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::lla2ecef_GRS80 (const Eigen::MatrixBase< Derived > &lla_position)
	Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates using GRS90.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::lla2ecef_WGS84 (const Eigen::MatrixBase< Derived > &lla_position)
	Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates using WGS84.

template<typename Derived >
Eigen::Quaternion< typename Derived::Scalar >	NAV::trafo::n_Quat_b (const Eigen::MatrixBase< Derived > &rollPitchYaw)
	Quaternion for rotations from body to navigation frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::n_Quat_b (Scalar roll, Scalar pitch, Scalar yaw)
	Quaternion for rotations from body to navigation frame.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::n_Quat_e (Scalar latitude, Scalar longitude)
	Quaternion for rotations from Earth-fixed to navigation frame.

template<typename DerivedA , typename DerivedB >
Eigen::Vector3< typename DerivedA::Scalar >	NAV::trafo::ned2ecef (const Eigen::MatrixBase< DerivedA > &n_position, const Eigen::MatrixBase< DerivedB > &lla_position_ref)
	Converts local NED coordinates into ECEF coordinates.

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Quaternion< Scalar >	NAV::trafo::p_Quat_b (Scalar mountingAngleX, Scalar mountingAngleY, Scalar mountingAngleZ)
	Quaternion for rotations from body to platform frame.

template<typename DerivedA , typename DerivedB >
Eigen::Vector3< typename DerivedA::Scalar >	NAV::trafo::pz90toWGS84 (const Eigen::MatrixBase< DerivedA > &pz90, const Eigen::MatrixBase< DerivedB > &pz90_pos)
	Converts PZ-90.11 vectors to WGS84 frame.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::pz90toWGS84_pos (const Eigen::MatrixBase< Derived > &pz90_pos)
	Converts PZ-90.11 coordinates to WGS84 coordinates.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::quat2eulerZYX (const Eigen::QuaternionBase< Derived > &q)
	Converts the quaternion to Euler rotation angles with rotation sequence ZYX.

template<typename Derived >
Eigen::Vector3< typename Derived::Scalar >	NAV::trafo::sph2ecef (const Eigen::MatrixBase< Derived > &position_s, const typename Derived::Scalar &elevation, const typename Derived::Scalar &azimuth)
	Converts spherical Earth-centered-Earth-fixed coordinates into cartesian coordinates.

Detailed Description

Transformation collection.

Author: T. Topp (topp@.nosp@m.ins..nosp@m.uni-s.nosp@m.tutt.nosp@m.gart..nosp@m.de)

Date: 2020-09-08

Coordinate Frames:

Inertial frame (i-frame) O_i: Earth center x_i: Direction to Vernal equinox y_i: In equatorial plane, complementing to Right-Hand-System z_i: Vertical on equatorial plane (North)
Earth-centered-Earth-fixed frame (e-frame) O_e: Earth center of mass x_e: Direction to Greenwich meridian (longitude = 0°) y_e: In equatorial plane, complementing to Right-Hand-System z_e: Vertical on equatorial plane (North)
Local Navigation frame (n-frame) O_n: Vehicle center of mass x_n: "North" y_n: Right-Hand-System ("East") z_n: Earth center ("Down")
Body frame (b-frame) O_b: Vehicle center of mass x_b: Roll-axis ("Forward") y_b: Pitch-axis ("Right") z_b: Yaw-axis ("Down")
Platform frame (p-frame) O_b: Center of IMU x_b: X-Axis Accelerometer/Gyrometer y_b: Y-Axis Accelerometer/Gyrometer z_b: Z-Axis Accelerometer/Gyrometer

Function Documentation

◆ b_Quat_n() [1/2]

template<typename Derived >

Eigen::Quaternion< typename Derived::Scalar > NAV::trafo::b_Quat_n ( const Eigen::MatrixBase< Derived > & rollPitchYaw )

Quaternion for rotations from navigation to body frame.

Parameters

[in] rollPitchYaw Roll, Pitch, Yaw angle in [rad]

Returns: The rotation Quaternion representation

◆ b_Quat_n() [2/2]

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::b_Quat_n	(	Scalar	roll,
		Scalar	pitch,
		Scalar	yaw )

Quaternion for rotations from navigation to body frame.

Parameters

[in]	roll	Roll angle in [rad]
[in]	pitch	Pitch angle in [rad]
[in]	yaw	Yaw angle in [rad]

Returns: The rotation Quaternion representation

◆ b_Quat_p()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::b_Quat_p	(	Scalar	mountingAngleX,
		Scalar	mountingAngleY,
		Scalar	mountingAngleZ )

Quaternion for rotations from platform to body frame.

Parameters

[in]	mountingAngleX	Mounting angle to x axis in [rad]. First rotation. (-pi:pi]
[in]	mountingAngleY	Mounting angle to y axis in [rad]. Second rotation. (-pi/2:pi/2]
[in]	mountingAngleZ	Mounting angle to z axis in [rad]. Third rotation. (-pi:pi]

Returns: The rotation Quaternion representation

◆ e_Quat_i()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::e_Quat_i	(	Scalar	time,
		Scalar	omega_ie = InsConst<Scalar>::omega_ie )

Quaternion for rotations from inertial to Earth-centered-Earth-fixed frame.

Parameters

[in]	time	Time (t - t0)
[in]	omega_ie	Angular velocity in [rad/s] of earth frame with regard to the inertial frame

Returns: The rotation Quaternion representation

◆ e_Quat_n()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::e_Quat_n	(	Scalar	latitude,
		Scalar	longitude )

Quaternion for rotations from navigation to Earth-fixed frame.

Parameters

[in]	latitude	𝜙 Geodetic latitude in [rad]
[in]	longitude	λ Geodetic longitude in [rad]

Returns: The rotation Quaternion representation

◆ ecef2lla()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::internal::ecef2lla	(	const Eigen::MatrixBase< Derived > &	e_position,
		typename Derived::Scalar	a,
		typename Derived::Scalar	b,
		typename Derived::Scalar	e_squared )

Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude.

Parameters

[in]	e_position	Vector with coordinates in ECEF frame in [m]
[in]	a	Semi-major axis of the reference ellipsoid
[in]	b	Semi-minor axis of the reference ellipsoid
[in]	e_squared	Square of the first eccentricity of the ellipsoid

Returns: Vector containing [latitude 𝜙, longitude λ, altitude]^T in [rad, rad, m]

Note: See See S. Gleason (2009) - GNSS Applications and Methods: Software example 'Chapter6_GNSS_INS_1/wgsxyz2lla.m' (J.A. Farrel and M. Barth, 1999, GPS & Inertal Navigation. McGraw-Hill. pp. 29.)

◆ ecef2lla_GRS80()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::ecef2lla_GRS80 ( const Eigen::MatrixBase< Derived > & e_position )

Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude using GRS90.

Parameters

[in] e_position Vector with coordinates in ECEF frame in [m]

Returns: Vector containing [latitude 𝜙, longitude λ, altitude]^T in [rad, rad, m]

◆ ecef2lla_WGS84()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::ecef2lla_WGS84 ( const Eigen::MatrixBase< Derived > & e_position )

Converts Earth-centered-Earth-fixed coordinates into latitude, longitude and altitude using WGS84.

Parameters

[in] e_position Vector with coordinates in ECEF frame

Returns: Vector containing [latitude 𝜙, longitude λ, altitude]^T in [rad, rad, m]

◆ ecef2ned()

template<typename DerivedA , typename DerivedB >

Eigen::Vector3< typename DerivedA::Scalar > NAV::trafo::ecef2ned	(	const Eigen::MatrixBase< DerivedA > &	e_position,
		const Eigen::MatrixBase< DerivedB > &	lla_position_ref )

Converts ECEF coordinates into local NED coordinates.

Parameters

[in]	e_position	ECEF coordinates in [m] to convert
[in]	lla_position_ref	Reference [𝜙 latitude, λ longitude, altitude]^T in [rad, rad, m] which represents the origin of the local frame

Returns: [x_N, x_E, x_D]^T Local NED coordinates in [m]

Note: See G. Cai, B.M. Chen, Lee, T.H. Lee, 2011, Unmanned Rotorcraft Systems. Springer. pp. 32

Attention: This function does not take the sphericity of the Earth into account

◆ i_Quat_e()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::i_Quat_e	(	Scalar	time,
		Scalar	omega_ie = InsConst<Scalar>::omega_ie )

Quaternion for rotations from Earth-centered-Earth-fixed to inertial frame.

Parameters

[in]	time	Time (t - t0)
[in]	omega_ie	Angular velocity in [rad/s] of earth frame with regard to the inertial frame

Returns: The rotation Quaternion representation

◆ lla2ecef()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::internal::lla2ecef	(	const Eigen::MatrixBase< Derived > &	lla_position,
		typename Derived::Scalar	a,
		typename Derived::Scalar	e_squared )

Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates.

Parameters

[in]	lla_position	[𝜙 latitude, λ longitude, altitude]^T in [rad, rad, m]
[in]	a	Semi-major axis of the reference ellipsoid
[in]	e_squared	Square of the first eccentricity of the ellipsoid

Returns: The ECEF coordinates in [m]

Note: See C. Jekeli, 2001, Inertial Navigation Systems with Geodetic Applications. pp. 23

◆ lla2ecef_GRS80()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::lla2ecef_GRS80 ( const Eigen::MatrixBase< Derived > & lla_position )

Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates using GRS90.

Parameters

[in] lla_position [𝜙 latitude, λ longitude, altitude]^T in [rad, rad, m]

Returns: The ECEF coordinates in [m]

◆ lla2ecef_WGS84()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::lla2ecef_WGS84 ( const Eigen::MatrixBase< Derived > & lla_position )

Converts latitude, longitude and altitude into Earth-centered-Earth-fixed coordinates using WGS84.

Parameters

[in] lla_position [𝜙 latitude, λ longitude, altitude]^T in [rad, rad, m]

Returns: The ECEF coordinates in [m]

◆ n_Quat_b() [1/2]

template<typename Derived >

Eigen::Quaternion< typename Derived::Scalar > NAV::trafo::n_Quat_b ( const Eigen::MatrixBase< Derived > & rollPitchYaw )

Quaternion for rotations from body to navigation frame.

Parameters

[in] rollPitchYaw Roll, Pitch, Yaw angle in [rad]

Returns: The rotation Quaternion representation

◆ n_Quat_b() [2/2]

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::n_Quat_b	(	Scalar	roll,
		Scalar	pitch,
		Scalar	yaw )

Quaternion for rotations from body to navigation frame.

Parameters

[in]	roll	Roll angle in [rad]
[in]	pitch	Pitch angle in [rad]
[in]	yaw	Yaw angle in [rad]

Returns: The rotation Quaternion representation

◆ n_Quat_e()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::n_Quat_e	(	Scalar	latitude,
		Scalar	longitude )

Quaternion for rotations from Earth-fixed to navigation frame.

Parameters

[in]	latitude	𝜙 Geodetic latitude in [rad]
[in]	longitude	λ Geodetic longitude in [rad]

Returns: The rotation Quaternion representation

◆ ned2ecef()

template<typename DerivedA , typename DerivedB >

Eigen::Vector3< typename DerivedA::Scalar > NAV::trafo::ned2ecef	(	const Eigen::MatrixBase< DerivedA > &	n_position,
		const Eigen::MatrixBase< DerivedB > &	lla_position_ref )

Converts local NED coordinates into ECEF coordinates.

Parameters

[in]	n_position	NED coordinates in [m] to convert
[in]	lla_position_ref	Reference [𝜙 latitude, λ longitude, altitude]^T in [rad, rad, m] which represents the origin of the local frame

Returns: ECEF position in [m]

Note: See G. Cai, B.M. Chen, Lee, T.H. Lee, 2011, Unmanned Rotorcraft Systems. Springer. pp. 32

Attention: This function does not take the sphericity of the Earth into account

◆ p_Quat_b()

template<typename Scalar , typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>

Eigen::Quaternion< Scalar > NAV::trafo::p_Quat_b	(	Scalar	mountingAngleX,
		Scalar	mountingAngleY,
		Scalar	mountingAngleZ )

Quaternion for rotations from body to platform frame.

Parameters

[in]	mountingAngleX	Mounting angle to x axis in [rad]. First rotation. (-pi:pi]
[in]	mountingAngleY	Mounting angle to y axis in [rad]. Second rotation. (-pi/2:pi/2]
[in]	mountingAngleZ	Mounting angle to z axis in [rad]. Third rotation. (-pi:pi]

Returns: The rotation Quaternion representation

◆ pz90toWGS84()

template<typename DerivedA , typename DerivedB >

Eigen::Vector3< typename DerivedA::Scalar > NAV::trafo::pz90toWGS84	(	const Eigen::MatrixBase< DerivedA > &	pz90,
		const Eigen::MatrixBase< DerivedB > &	pz90_pos )

Converts PZ-90.11 vectors to WGS84 frame.

Parameters

[in]	pz90	Vector in PZ-90.11 frame
[in]	pz90_pos	Position in PZ-90.11 frame (needed for calculation)

Returns: Vector in WGS84 frame

◆ pz90toWGS84_pos()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::pz90toWGS84_pos ( const Eigen::MatrixBase< Derived > & pz90_pos )

Converts PZ-90.11 coordinates to WGS84 coordinates.

Parameters

[in] pz90_pos Position in PZ-90.11 coordinates

Returns: Position in WGS84 coordinates

Note: See [35] PZ-90.11 Reference Document Appendix 4, p.34f

◆ quat2eulerZYX()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::quat2eulerZYX ( const Eigen::QuaternionBase< Derived > & q )

Converts the quaternion to Euler rotation angles with rotation sequence ZYX.

Parameters

[in] q Quaternion to convert

Returns: [angleX, angleY, angleZ]^T vector in [rad]. The returned angles are in the ranges (-pi:pi] x (-pi/2:pi/2] x (-pi:pi]

◆ sph2ecef()

template<typename Derived >

Eigen::Vector3< typename Derived::Scalar > NAV::trafo::sph2ecef	(	const Eigen::MatrixBase< Derived > &	position_s,
		const typename Derived::Scalar &	elevation,
		const typename Derived::Scalar &	azimuth )

Converts spherical Earth-centered-Earth-fixed coordinates into cartesian coordinates.

Parameters

[in]	position_s	Position in spherical coordinates to convert
[in]	elevation	Elevation in [rad]
[in]	azimuth	Azimuth in [rad]

Returns: The ECEF coordinates in [m]

Functions

Detailed Description

Function Documentation

◆ b_Quat_n() [1/2]

◆ b_Quat_n() [2/2]

◆ b_Quat_p()

◆ e_Quat_i()

◆ e_Quat_n()

◆ ecef2lla()

◆ ecef2lla_GRS80()

◆ ecef2lla_WGS84()

◆ ecef2ned()

◆ i_Quat_e()

◆ lla2ecef()

◆ lla2ecef_GRS80()

◆ lla2ecef_WGS84()

◆ n_Quat_b() [1/2]

◆ n_Quat_b() [2/2]

◆ n_Quat_e()

◆ ned2ecef()

◆ p_Quat_b()

◆ pz90toWGS84()

◆ pz90toWGS84_pos()

◆ quat2eulerZYX()

◆ sph2ecef()